A new enhanced assumed strain quadrilateral membrane element with drilling degree of freedom and modified shape functions

Boutagouga, Djamel

doi:10.1002/nme.5430

Cited by 17 publications

(8 citation statements)

References 58 publications

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“…Since then, many efforts have been put on developing membrane elements with drilling DOFs. Recent attempts include but are not limited to the literatures …”

Section: Introductionsupporting

confidence: 57%

“…Recent attempts include but are not limited to the literatures. [50][51][52][53][54][55] In the present work, a simple but robust unsymmetric 4-node low-order quadrilateral membrane element with the drilling DOFs is developed. First, the test function of this element is assumed as a new kind of 2-dimensional isoparametric-based displacement field enriched by the drilling DOFs.…”

Section: Introductionmentioning

confidence: 99%

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4‐node unsymmetric quadrilateral membrane element with drilling DOFs insensitive to severe mesh‐distortion

Shang

Ouyang

2017

Numerical Meth Engineering

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Summary The unsymmetric finite element method is a promising technique to produce distortion‐immune finite elements. In this work, a simple but robust 4‐node 12‐DOF unsymmetric quadrilateral membrane element is formulated. The test function of this new element is determined by a concise isoparametric‐based displacement field that is enriched by the Allman‐type drilling degrees of freedom. Meanwhile, a rational stress field, instead of the displacement one in the original unsymmetric formulation, is directly adopted to be the element's trial function. This stress field is obtained based on the analytical solutions of the plane stress/strain problem and the quasi‐conforming technique. Thus, it can a priori satisfy related governing equations. Numerical tests show that the presented new unsymmetric element, named as US‐Q4θ, exhibits excellent capabilities in predicting results of both displacement and stress, in most cases, superior to other existing 4‐node element models. In particular, it can still work very well in severely distorted meshes even when the element shape deteriorates into concave quadrangle or degenerated triangle.

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“…Since then, many efforts have been put on developing membrane elements with drilling DOFs. Recent attempts include but are not limited to the literatures …”

Section: Introductionsupporting

confidence: 57%

Section: Introductionmentioning

confidence: 99%

4‐node unsymmetric quadrilateral membrane element with drilling DOFs insensitive to severe mesh‐distortion

Shang

Ouyang

2017

Numerical Meth Engineering

View full text Add to dashboard Cite

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“…Previous research mainly provides two simple definitions of the drilling DoF : (i) nodal rigid body rotation 10 and (ii) skew part of strain tensor (eg, related works 16,[18][19][20]33 ). However, those definitions have their own limitations, especially when it comes to the fully-fixed boundary condition, in which case, both fail to give zero value for drilling DoF.…”

Section: Definition Of Dofsmentioning

confidence: 99%

A new drilling quadrilateral membrane element with high coarse‐mesh accuracy using a modified Hu‐Washizu principle

Chang

Lee

Carr

et al. 2019

Numerical Meth Engineering

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Summary By utilizing a modified Hu‐Washizu principle, a new mixed variational framework and a corresponding high‐performing four‐node membrane element with drilling degrees of freedom, named as GCMQ element, are proposed. In this work, the generalized conforming concept, which is originally proposed within a displacement‐based formulation, is extended to a mixed formulation. The new element is able to handle higher‐order displacement, strain, and stress distributions. The interpolations are complete up to second order for stress and strain. The enhanced strain field is optimized so that a complete cubic displacement field can be represented. For numerical integration, a five‐point scheme is proposed to minimize computational cost. Compared to other four‐node elements in existing literature, numerical examples show that the proposed element has a better performance regarding predictions of both displacements and internal forces, particularly with coarse meshes. The new element is also free from shear locking and volumetric locking. Due to the nature of the mixed framework, GCMQ can be directly used in elastoplastic applications.

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“…A topic which has attracted the attention of researchers is to include drilling degree of freedom in their shell elements. In the past decades, plane elements with drilling degree of freedom were widely developed to use in the linear and nonlinear analysis of plane structures [26][27][28][29]. Gradually, this subject was considered in shell elements.…”

Section: Introductionmentioning

confidence: 99%

A 6-parameter triangular flat shell element for nonlinear analysis

Rezaiee‐Pajand

Masoodi

Arabi

2019

TECM

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In this paper, an improved flat triangular shell element is proposed. This element has three nodes, and in each node, six degrees of freedom are considered. Since there are three rotational degrees of freedom at each node, the drilling effect can be incorporated in authors' formulation. A new procedure is also suggested for updating the director vectors about which the rotational degrees of freedom are defined. In order to study large displacements and rotations, Total Lagrangian principles are employed. In addition, updating the rotational degrees of freedom is implemented using enriched updated director vectors, which are formulated based on the finite rotation method. On the other hand, small strains are considered in this formulation. By utilizing MITC method, shear and membrane locking is mitigated from new element. To examine the performance, the element passes three basic tests, including isotropy, and patch test. Moreover, a convergence study is also implemented to show the elemental behavior. Several popular benchmarks are considered to illustrate the accuracy and capability of the suggested element in geometrically nonlinear analyses.

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A new enhanced assumed strain quadrilateral membrane element with drilling degree of freedom and modified shape functions

Cited by 17 publications

References 58 publications

4‐node unsymmetric quadrilateral membrane element with drilling DOFs insensitive to severe mesh‐distortion

4‐node unsymmetric quadrilateral membrane element with drilling DOFs insensitive to severe mesh‐distortion

A new drilling quadrilateral membrane element with high coarse‐mesh accuracy using a modified Hu‐Washizu principle

A 6-parameter triangular flat shell element for nonlinear analysis

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